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Name of NGM Educator:

William Trapp, Business Math, Cheney Technical High School

Name of Host Company:

Pratt & Whitney, United Technologies, Inc.

Grade Level:

12th grade

Student Work Types:

Type One:

Present a picture of a machined part. Show two sets of data representing measurements of one key dimension. Ask class which is the best set of data.

From lists shown on smartboard, have class calculate mean, median and mode. Explain this is probably review but these are some measures businesses and others use to help make decisions. Also they will calculate more of these from a worksheet for homework.

Type 2

Put up picture and data sets from previous day. Remind students of their opinions about which set of data is better. Tell them we'll study one way of measuring variance today: standard deviation.  Using mean from day 1 calculations, lead students through the steps to calculate the standard deviations for both sets of data.. When they finish, put formula for standard deviation on board and explain that this is what they just did. If I had put this up first, the class would have been scared off by the complex looking formula. Explain the sigma (summation) notation by using as simple example. After calculating standard deviation for the data sets on the smartboard, class will work out a few more from a teacher generated sheet. Some of these will be done as homework .

Type 3

Put up slide of large data set. Remind class of the complicated calculations we did previously to find standard deviation of a small data set. Ask if they'd like to do the same with this big set? Tell them help is available. Hand out TI-83's. Put up data sets with 25 entries on smartboard. Demonstrate process to create lists in the calculator. Then use calculator to compute mean and standard deviation. Class will practice on data sets from teacher generated worksheet. Examples not completed in class will be assigned as homework.

Type 4

Ask students to recall previous day's work. (Put slide of data on smartboard). Ask if they think in this time of technological breakthroughs if they think standard deviations are calculated by people using TI-83's on a regular basis. Tell them there's a better way: Ask class if anyone is familiar with the program Excel? To those who answer positively, ask for a volunteer to give a brief description to the rest of the class. Explain that Excel is a spreadsheet application but that it has tools which allow you to easily calculate statistics. Put up slide of same data set as previous lesson but now in Excel format. Demonstrate easy process for calculating mean and standard deviation. Let volunteers practice on other data sets. If available, assign data sets to be worked on in computer lab. 

Type 5

Present data on real costs associated with rejected parts. Show how these costs increase as part goes farther and farther through the system. Ask class for ideas on what some of these costs might be. (Possible answers: repairing part or having to make it again, holding up other workers, late delivery to customer, failure of finished product that part goes into. Put up slide of FAA account of Delta flight where engine failed killing 2 passengers. Tell class this could be one of the costs just mentioned. Say that modern factories use statistics to keep processes in control to minimize chances of bad parts being produced. This is in contrast to the old way of inspecting final part to be sure it meets design criteria. Demonstrate calculations for Cpu and Cpl using data sets and formulae from slides on smartboard. Stress that the inputs to this process are either values you can look up on a blueprint or are calculated like we've done before. Therefore, we have knowledge right now to make these calculations!! Using several data columns for the same part, have class calculate mean and standard deviation for each list, then calculate Cpu and Cpl for each. Explain that Cpk is just the smallest value of these for each pair of calculations. Knowing what they know about variance and standard deviation, ask for opinions about which Cpk is the best out of the ones they've calculated. (Higher number is better). Put up slide relating Cpk levels with rejections per million. Tell the class that what we've been doing over the past few days relates directly to what companies are doing to improve their processes and lower their costs. This makes them stronger companies and, hence, better places to work.

Type 6

Present catapult to class (it can be made by the class if time allows). Explain its operation and how several settings can be changed. Tell class we're going to make teams and launch the ball 25 times recording carefully how far it goes. Each team uses catapult to launch the ball 25 times and records how far it goes. Uses Excel, they will create a spreadsheet and calculate mean and standard deviation. Using formulae, etc. they can also use the spreadsheet to calculate Cpl, Cpu and Cpk given reasonable design limits by the instructor. Based on different settings of the catapult, teams will record their findings on the board. We can use these to decide how well the process is in control. Once data is compared, ask students for ideas about how we would go about improving the process to make it more consistent.Watch for techniques when launching ball, measuring distance and recording data. Also check to make sure calculations seem to make sense. Listen for responses about improving the process. Review entire process improvement process. Explain there is lots more to this and that there are books to read or websites that provide more information if they want to learn more.

Task Abstract: Students will start with mean and standard deviation calculations for simple data sets. They will progress through larger data sets using modern tools (TI-83 and Excel) to do the difficult computations. They will begin to appreciate that normally in similar data sets lower variance is good. Finally they will relate these abstract calculations to real world process controls and see how this can save companies lots of money.

Task Objectives: Students will be able to hand calculate mean and standard deviation for small data sets. They will learn how to use TI-83's and Excel as assists to do these computations on larger data sets. Finally they will learn the basics of Cpk calculations and see how this relates to modern manufacturing companies and building quality products.

Esssential Understandings/Questions:

The math behind these concepts is not that difficult. Once lists are made, using modern tools mean and standard deviation calculations are not difficult. These figures along with tolerances are directly related to the numbers of bad parts a company will produce.

Task Description: Students will progress from basic statistics to large data lists using calculators or spreadsheet applications. They then can take this newly learned knowledge and apply in the exact same way someone at a Connecticut manufacturing company would.

Resources Required:

A Smartboard, TI-83 calculators, computers with Excel and data sets derived from actual examples from my internship. Also a simple catapult to generate data with variation.

Prior Learning Required:

From prior algebra courses, students should have learned the basics of statistics.

The visual aids such as Smartboard slides, Excel spreadsheets and the catapult should help special needs students and those whose learning styles favor visual or tactile stimulation.

Educator Comments: I am hoping that working with data from real world applications will motivate student learning. I think some of this will sneak up on some of the students and they'll be doing fairly complicated computations before they realize it. I also want to impress on them that this is how successful companies are actually doing things right now and that some of this knowledge will make them more valuable when they are looking for careers.